Spectral models attempt to parameterize sound at the basilar membrane
of the ear. Thus, sound representations and transformations in these
models should be closely linked to the perception. Among those
models, sinusoidal modeling deals with partials that are
pseudo-sinusoidal tracks for which frequencies and amplitudes
continuously evolve slowly with time. This is a generalization of
additive (modal) synthesis, and is also related to the physical
structure of the sounds. Sinusoidal modeling is extremely useful for
many applications such as musical sound transformation (time scaling,
pitch shifting, re-spatialization, etc.), coding (compression), and
also classification.

Apart from the extension to the non-stationary case, one recent
research direction with sinusoidal modeling is the modeling of the
parameters of the partials themselves. By re-analyzing the evolutions
of the model parameters, we obtain (level-2) parameters of a
hierarchical model well-suited for time scaling while preserving
musical modulations such as vibrato and tremolo. Moreover, the
reanalysis of the spectral parameters turns out to be extremely useful
for difficult problems such as lossless compression or source
separation for example. An impressive application is "active
listening", enabling the user to interact with the sound while it is
played. The musical parameters (loudness, pitch, timbre, duration,
spatial location) of the sound entities (sources) present in the
musical mix can thus be changed interactively.

About spectral representations for digital images...

IBISA (Image-Based Identification/Search for Archaeology)
manages databases of digital images of archaeological
objects, and allows the user to perform searches by examples.
The objects are only required to be quasi flat (two-dimensional) and
produced from matrices via some striking / stamping / casting process.
The original matrices are generally lost now, but many objects with
their prints can still be found, with many similarities among them.
For now, the system works with ancient (greek, roman) coins, and the
generalization to medieval tiles is under progress.

IBISA was designed to help the user decide, from their images,
if two objects are either the same, come from the same matrix,
share resemblance in style, or are completely different.
It uses computer vision methods to make this decision while getting
rid of the viewing conditions when searching for similarities in the
databases. First, a segmentation method based on active contours
extracts the useful part of each image from its background context.
Then, a registration method based on the Fourier-Mellin transform
sorts the images by similarity, canceling any translation, rotation,
or zoom inherent to the photography.